z i:SrSSKJr SSKJr SSKrSSKJr SSKJ r SSK J r SSK J r SS KJr "S S \ 5r"S S \5r"SS\5rg)zU1 Gate.) annotations)expN)ControlledGate)Gate)ParameterValueType)_ctrl_state_to_int) StandardGatec^\rSrSrSr\R rS S U4SjjjrSr S S U4Sjjjr SSSjjr SSjr Sr S rU=r$)U1Gateu#Single-qubit rotation about the Z axis. This is a diagonal gate. It can be implemented virtually in hardware via framechanges (i.e. at zero error and duration). .. warning:: This gate is deprecated. Instead, the following replacements should be used .. math:: U1(\theta) = P(\theta)= U(0,0,\theta) .. code-block:: python circuit = QuantumCircuit(1) circuit.p(lambda, 0) # or circuit.u(0, 0, lambda, 0) Circuit symbol: .. code-block:: text ┌───────┐ q_0: ┤ U1(θ) ├ └───────┘ Matrix representation: .. math:: U1(\theta) = \begin{pmatrix} 1 & 0 \\ 0 & e^{i\theta} \end{pmatrix} Examples: .. math:: U1(\theta = \pi) = Z .. math:: U1(\theta = \pi/2) = S .. math:: U1(\theta = \pi/4) = T .. seealso:: :class:`~qiskit.circuit.library.standard_gates.RZGate`: This gate is equivalent to RZ up to a phase factor. .. math:: U1(\theta) = e^{i{\theta}/2} RZ(\theta) :class:`~qiskit.circuit.library.standard_gates.U3Gate`: U3 is a generalization of U2 that covers all single-qubit rotations, using two X90 pulses. Reference for virtual Z gate implementation: `1612.00858 `_ c(>[TU]SSU/US9 g)zQ Args: theta: The rotation angle. label: An optional label for the gate. u1labelN)super__init__)selfthetar __class__s b/home/james-whalen/.local/lib/python3.13/site-packages/qiskit/circuit/library/standard_gates/u1.pyrU1Gate.__init__^s q5'7cSSKJn UR[RR UR 5SURS9UlgzDefault definitionr)QuantumCircuitT) legacy_qubitsnameN) qiskit.circuitr_from_circuit_datar U1_get_definitionparamsr definitionrrs r_defineU1Gate._definefsA 2 );; OO + +DKK 8SWS\S\< rc2>U(d:US:Xa4[URSX#S9nURURlU$U(d=Uc:US:a4[ URSXS9nURURlU$[ TU]UUUUS9nU$)aReturn a (multi-)controlled-U1 gate. Args: num_ctrl_qubits: number of control qubits. label: An optional label for the gate [Default: ``None``] ctrl_state: control state expressed as integer, string (e.g.``'110'``), or ``None``. If ``None``, use all 1s. annotated: indicates whether the controlled gate should be implemented as an annotated gate. Returns: ControlledGate: controlled version of this gate. rr)r ctrl_staternum_ctrl_qubitsrr) annotated)CU1Gater#r base_gateMCU1Gatercontrolrr+rr)r,gaters rr0U1Gate.controlss(_14;;q>ND#'::DNN  z1o6IDKKNOID#'::DNN  7? /%# #D  rc4[URS*5$)aReturn inverted U1 gate (:math:`U1(\lambda)^{\dagger} = U1(-\lambda))` Args: annotated: when set to ``True``, this is typically used to return an :class:`.AnnotatedOperation` with an inverse modifier set instead of a concrete :class:`.Gate`. However, for this class this argument is ignored as the inverse of this gate is always a :class:`.U1Gate` with inverse parameter values. Returns: U1Gate: inverse gate. r)r r#rr,s rinverseU1Gate.inversest{{1~o&&rcUSLa [S5e[URS5n[R"SS/S[R "SU-5//US9$)z%Return a numpy.array for the U1 gate.F9unable to avoid copy while creating an array as requestedrr?dtype) ValueErrorfloatr#numpyarrayr)rr<copylams r __array__U1Gate.__array__sS 5=XY YDKKN#{{QFQ "s((;$<=UKKrcR[U[5=(a URU5$N) isinstancer _compare_parametersrothers r__eq__ U1Gate.__eq__s%(LT-E-Ee-LLrr$rF)rrr str | NonerNNFr+intrrNr)str | int | Noner,boolFr,rSNN)__name__ __module__ __qualname____firstlineno____doc__r r!_standard_gaterr&r0r6rCrK__static_attributes__ __classcell__rs@rr r szAF"__N88   ! '+ !!!% !  !!F 'LMMrr c^\rSrSrSr\R rS SS.S U4SjjjjrSr SSU4Sjjjr SSSjjr S S jr S r S rU=r$)r-uControlled-U1 gate. This is a diagonal and symmetric gate that induces a phase on the state of the target qubit, depending on the control state. .. warning:: This gate is deprecated. Instead, the :class:`.CPhaseGate` should be used .. math:: CU1(\lambda) = CP(\lambda) .. code-block:: python circuit = QuantumCircuit(2) circuit.cp(lambda, 0, 1) Circuit symbol: .. code-block:: text q_0: ─■── │θ q_1: ─■── Matrix representation: .. math:: CU1(\theta) = I \otimes |0\rangle\langle 0| + U1 \otimes |1\rangle\langle 1| = \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & e^{i\theta} \end{pmatrix} .. seealso:: :class:`~qiskit.circuit.library.standard_gates.CRZGate`: Due to the global phase difference in the matrix definitions of U1 and RZ, CU1 and CRZ are different gates with a relative phase difference. N _base_labelc <>[TU]SSU/SUU[XS9S9 g)zCreate new CU1 gate.cu1rrr+rr)r.Nrrr )rrrr)rcrs rrCU1Gate.__init__s3   G!U6  rcSSKJn UR[RR UR 5SURS9Ulgr) rrr r CU1r"r#rr$r%s rr&CU1Gate._definesC 2);;    , ,T[[ 9TXT]T]< rc>U(d;Uc8[URSUS-US9nURURlU$[TU]UUUUS9nU$)Controlled version of this gate. Args: num_ctrl_qubits: number of control qubits. label: An optional label for the gate [Default: ``None``] ctrl_state: control state expressed as integer, string (e.g.``'110'``), or ``None``. If ``None``, use all 1s. annotated: indicates whether the controlled gate should be implemented as an annotated gate. Returns: ControlledGate: controlled version of this gate. rr)r+rr*)r/r#rr.rr0r1s rr0CU1Gate.controlsh(Z/DKKNOar#r)r?r@)rr<rAeiths rrCCU1Gate.__array__7s 5=XY Y2dkk!n--. ??;;|\Aq!T?KSX ;;|aD!_lKSX rc[U[5=(a1 URUR:H=(a URU5$rF)rGr-r)rHrIs rrKCU1Gate.__eq__Es; ug & 05#3#33 0((/ rrMrV)rrrrNr)rRrOrPrTrU)rWrXrYrZr[r rkr\rr&r0r6rCrKr]r^r_s@rr-r-s2h"%%N !'+    !  %   &  " ! '+ %   @ D   rr-c^\rSrSrSrS SS.S U4SjjjjrSrS SU4SjjjrSSSjjrS r S r U=r $)r/iMuFMulti-controlled-U1 gate. This is a diagonal and symmetric gate that induces a phase on the state of the target qubit, depending on the state of the control qubits. .. warning:: This gate is deprecated. Instead, the following replacements should be used .. math:: MCU1(\lambda) = MCP(\lambda) .. code-block:: python circuit = QuantumCircuit(5) circuit.mcp(lambda, list(range(4)), 4) Circuit symbol: .. code-block:: text q_0: ────■──── │ . │ q_(n-1): ────■──── ┌───┴───┐ q_n: ┤ U1(λ) ├ └───────┘ .. seealso:: :class:`~qiskit.circuit.library.standard_gates.CU1Gate`: The singly-controlled-version of this gate. Nrbc B>[TU]SUS-U/UUU[XS9S9 g)zCreate new MCU1 gate.mcu1rrrgNrh)rrBr+rr)rcrs rrMCU1Gate.__init__vs8   a  E+!S4  rc<URS:Xa#[URS5RnOcURS:Xa#[ URS5RnO0SSKJn U"URSUR5RnXlg)Nrr) MCPhaseGate)r+r r#r$r-pr|)rr$r|s rr&MCU1Gate._definesv   1 $ A/::J  ! !Q & Q0;;J &$T[[^T5I5IJUUJ$rc>U(d_[X15nURU-U-n[URSXR-UUS9nUR UR lU$[TU]!UUUUS9nU$)rnr)r+rr)r*) rr)r/r#r+rr.rr0)rr+rr)r,new_ctrl_stater2rs rr0MCU1Gate.controls(+JHJ"oo@JNN A /2F2F F) D $(::DNN  7? /%# #D  rc\[URS*URURS9$)aReturn inverted MCU1 gate (:math:`MCU1(\lambda)^{\dagger} = MCU1(-\lambda))` Args: annotated: when set to ``True``, this is typically used to return an :class:`.AnnotatedOperation` with an inverse modifier set instead of a concrete :class:`.Gate`. However, for this class this argument is ignored as the inverse of this gate is always a :class:`.MCU1Gate` with inverse parameter values. Returns: MCU1Gate: inverse gate. r)r+r))r/r#r+r)r5s rr6MCU1Gate.inverses, [[^OT-A-Adoo  rc[U[5=(aQ URUR:H=(a1 URUR:H=(a UR U5$rF)rGr/r+r)rHrIs rrKMCU1Gate.__eq__sV uh ' 0$$(=(== 05#3#33 0((/  rrMrV)rBrr+rQrrNr)rRrOrPrTrU) rWrXrYrZr[rr&r0r6rKr]r^r_s@rr/r/Ms&X!'+       %   ( % ! '+ %%%% %  %%N "  rr/)r[ __future__rcmathrr?qiskit.circuit.controlledgaterqiskit.circuit.gater"qiskit.circuit.parameterexpressionrqiskit.circuit._utilsrqiskit._accelerate.circuitr r r-r/rrrsP" 8$A43TMTTMn[ n[ |H ~H r